While most of us usually just set our phones to vibrate when we need some quiet there are alternatives. The latest to hit the scene is a free Do Not Disturb app by SRID games. You simply set a time for your phone to go silent and it will silence your email and phone notifications during that time. It also allows you to setup a white or blacklist of calls that can or cannot go through. While there are some more sophisticated apps this one definitely gets the job done. It also works great if you want to block out dinner time as family time every day.
Check out Do Not Disturb free in App World